You start to depreciate the improvement when they are "placed in service". "Placed in service" means when they are ready and available for business use.
For example, if all of the apartments were finished approximately the same time, you would depreciate it all when completed. But if you finished one apartment at a time, you would do the depreciation in 'chunks' when each unit was "placed in service".
Does that make sense?
As a side note, you will need to determine how long the building and improvements are depreciated. Although "Residential Rental Property" is depreciated over 27.5 years, as a mixed-use building, everything is probably depreciated over 39 years.
The determining factor is that if 80% of the total building rents are for Residential Dwelling Units, then the entire building and improvements are deprecated over 27.5 years. If it does not meet the 80% test, the entire building and improvements are depreciated over 39 years.
